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QUICK ANSWER
"Por qué" is a form of "por qué", a phrase which is often translated as "why". "Por qué no" is a form of "por qué no", a phrase which is often translated as "why not". Learn more about the difference between "por qué" and "por qué no" below.
por qué(
pohr
keh
)A phrase is a group of words commonly used together (e.g., once upon a time).
A masculine noun is used with masculine articles and adjectives (e.g., el hombre guapo, el sol amarillo).
por qué no(
pohr
keh
noh
)A phrase is a group of words commonly used together (e.g., once upon a time).
a. why not
Por qué no bañarse de noche en el lago. A mí me parece una gran idea. - A mí también.Why not go for a swim at night in the lake at night. I think it's a great idea. - Me too.
b. why not?
¿Te apetece cenar conmigo esta noche? - Sí, por qué no.Do you feel like having dinner with me tonight? - Yes, why not?
a. no direct translation
This refers to an idiomatic word or phrase for which there is no word-for-word translation.
No sé por qué no le pides a Claudio que te invite a cenar. Seguro que dice que sí.I don't know why you don't ask Claudio to take you to dinner. He'll surely say yes.
¿Por qué no quieres venir con nosotros, Lisa?Why don't you want to come with us, Lisa?